PDEs cracked by Artificial Intelligence at Cal Tech

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Discussion Overview

The discussion revolves around the application of artificial intelligence (AI) in solving partial differential equations (PDEs), particularly in the context of a method developed at the California Institute of Technology. Participants explore the implications of this technology, its capabilities, and the nature of the AI's problem-solving approach.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants highlight the significant speed-up achieved by the AI, claiming it can solve PDEs, like the Navier-Stokes equation, 1,000 times faster than traditional methods.
  • Others mention the use of genetic algorithms in AI systems, such as Eureqa, to derive equations of motion from data, suggesting a different approach to solving similar problems.
  • A participant questions whether the AI actually solves the equations or merely approximates solutions, raising concerns about the clarity of the results produced.
  • One viewpoint argues that the term "AI" may be misleading, suggesting that the process is more about function approximation rather than true intelligence.
  • Another participant notes that while AI may struggle with mathematical proofs, its ability to predict chaotic behavior could still represent a significant advancement, drawing parallels with AI applications in medicine.

Areas of Agreement / Disagreement

Participants express a mix of enthusiasm and skepticism regarding the capabilities of AI in solving PDEs. There is no consensus on the nature of the AI's problem-solving ability, with differing opinions on whether it constitutes true intelligence or merely function approximation.

Contextual Notes

Some claims about the AI's capabilities depend on specific definitions of intelligence and problem-solving, and there are unresolved questions about the explicitness of the solutions provided by the AI.

Tom.G
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With a 1000 time speed-up too, this could be a game-changer.

From: https://www.technologyreview.com/20...er-stokes-and-partial-differential-equations/

They did it by solving in "...Fourier space (rather) than to wrangle with PDEs in Euclidean space, which greatly simplifies the neural network’s job.

...capable of solving entire families of PDEs—such as the Navier-Stokes equation for any type of fluid—without needing retraining. Finally, it is 1,000 times faster than traditional mathematical formulas...

The full paper from The California Institute of Technology:
https://arxiv.org/pdf/2010.08895.pdf

Cheers,
Tom
 
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Interesting notion. The Eureqa software used extensive data and a genetic algorithm to discern the equations of motion of a compound pendulum.

This AI system uses the images to identify the equation's form and then goes from there.
 
I couldn't help but notice the lack of an explicit formula for the equations. Did an AI actually solve them or just approximate the solution implicitly on its own?
 
IMO it's not really "AI". It is function approximation, there is nothing intelligent about it. The natural intelligence of the researchers is real.
 
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Seems AI have trouble with math proofs atm, but if they can predict chaotic behavior better than people can it's still a significant step. The same issue occurs in medicine where doctors aren't given information by AI as to how it recognizes cancer and heart disease sooner than they can.
 

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